I intentionally phrased the question title a bit provocatively. What I mean is this: Aperture priority mode (Av) means that I select an aperture, and the camera selects the corresponding shutter speed. Shutter priority mode (Tv) means that I select a shutter speed, and the camera selects the corresponding aperture. Right?

So, for a given static scene, by me selecting any given aperture in Av, the CPU sets a corresponding shutter speed. And by me selecting any given shutter speed in Tv, the CPU sets a corresponding aperture.

Can someone please explain to me how the two things are any different?

Indeed, when I try it out (I have two different EOS Cameras, both are 35mm film SLRs: EOS Rebel Ti and EOS 620), I get either exactly the same, or very similar, shutter speed / aperture value combinations, regardless of whether I'm in Av or Tv (for the same static scene on a tripod, with static light). I can even set Av and "pretend" I'm in Tv, and the other way 'round.

So why are there two different modes or what's the difference between them? And isn't Program Shift, too, essentially the same for all practical intents and purposes?

I'd recommend not making the title so combative. I think you have a question there that doesn't really require that.
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John Cavan♦Mar 29 '13 at 15:16

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Now apply that logic to the arguement of "I believe the gas pedal and the brake pedal are essentially the same - prove me wrong!" ...........
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GaptonMar 29 '13 at 15:35

Thinking of the exposure triangle with the perimeter representing the exposure, once you fix the length of two sides (ISO and either the shutter speed or aperture), the third doesn't have much leeway, does it?
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ab.adityaMar 29 '13 at 16:19

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Also note that if you're shooting with manual flash and automatic exposure, aperture priority is the only mode that makes any sense whatsoever.
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Dietrich EppMar 29 '13 at 23:02

6 Answers
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Correct. As a matter of fact, on most cameras Program Shift is the same too by your logic.

These modes, including Program, are designed to give you the same exposure which is why the results are the same since Aperture and Shutter-Speed are inversely related given a fixed ISO.

The difference is what you decide on. Only you can decide if you would like a photo to have a particular depth-of-field or freeze/blur certain motion. You could attempt and guess what shutter-speed will give you the aperture with the depth-of-field you want, but is it not easier to simply choose the aperture?

You may note this in the behavior of the camera. In Aperture-Priority, the camera displays the chosen aperture at all times and the shutter-speed appears when the camera meters, usually on the half-press of by pressing AE-L (Oddly marked by * on Canon).

In fact, the procedure for getting an high shutter speed on the aperture priority only Electro Yashicas went by "set the widest aperture and decrease it until the overexposure warning light just turns off", implying the camera would be set to something very close to its top speed of 1/500.
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RyccardoMar 30 '13 at 14:54

So why are there two different modes or what's the difference between them?

Because trying to control aperture by setting the shutter speed and trying to predict what aperture the camera will choose is impractical. When you're taking a portrait, for example, you might want to choose a specific aperture. You can adjust the shutter speed in Tv mode until you find the aperture you want, but if the light changes a bit the camera may choose some other aperture. Av mode tells the camera to use the aperture that you've selected, no matter what.

Likewise, if you're shooting your kid's soccer game, you probably want to select very short exposures in order to stop the action, and you don't want the camera deciding to drop from 1/500 to 1/60 just because you pointed the camera in a different direction or a cloud obscured the sun, and you don't want to have to constantly fiddle with the aperture every time you compose a shot. Tv mode lets you give the shutter speed priority over aperture.

You are essentially correct in a simple case. It is really simply a convenience thing, though it does make a difference when dealing with more than 2 parameters. Don't think of it in terms of what the computer is doing, but what the person is doing.

If I want to have control of the depth of field for creative reasons, I will choose Av. If I happen to have ISO set to automatic as well, then the camera will know to keep the Av at my choice, but can choose to alter the other two parameters as necessary for a good shot.

On the other hand, if I am shooting something with fast motion or where I want to capture motion as blur, then I will want control of the shutter and not care so much about the depth of field. I can then use Tv and let the camera decide on Aperture and ISO.

If I need control of both, then I can use full manual and adjust it to my needs specifically.

Aperture Priority (Av) and Shutter Priority (Tv) only produce the same result if you choose the corresponding value after changing modes.

Say you meter a scene in Av mode with f/5.6 selected and the camera selects 1/60 sec. If you switch to Tv mode, select 1/60 sec and meter the same scene, the camera will of course select f/5.6. But if you select 1/1000 sec as your shutter speed the camera will select f/1.4 for the same scene. But wait, your lens' maximum aperture is f/2.8! What now? If you have safety shift enabled, the camera will use f/2.8 and lower the Tv to 1/250 sec. Although this is the same exposure value as 1/60 sec @ f/5.6, the resulting photo will be very different: The depth of field will be shallower and any objects in motion will show less movement.

Especially when shooting in dimmer light at low ISO sensitivity, the number of viable options are reduced by your lens' maximum aperture. As with almost everything in photography, the more light you have available, the more options you have for how you want your photo to appear.

They allow you to make different creative decisions. Take Av (aperture mode), if you are creating a portrait, you will likely want a large aperture for a flattering shallow depth of field, so maybe you set it to f2.8 and let the camera figure out the best shutter speed.

However, if you want to create a landscape, you want most of the image in focus, so you choose f11, and again let the camera choose the best shutter speed.

If however, you are shooting a sports scene, shutter speed becomes critical so you switch to Tv (time value) mode and set your shutter to 1/250, letting the camera choose the smallest aperture possible. In bright light that might be f5.6, but in low like it might be f2.8.

On the other hand, if you want to take a creative shot of dancers where you want to create some motion blur, you might choose 1/15.

It all depends on what your creative goal is, balanced with the lighting conditions you are faced with. In certain conditions both modes may produce similar or identical exposure values (like low-light shooting where your aperture will usually be wide open, no matter what), but you get to decide whats important.

I think what you're saying is that the camera will pick the same total exposure in either mode. For example: Suppose you're in aperture priority mode with f/8 selected. The camera picks a shutter speed of 1/250 second. If you then switch to shutter priority mode and select a shutter speed of 1/250 second, you find that the camera picks an aperture of f/8. This is certainly true, and intended. The camera meters the scene, determines what exposure it thinks is correct, and selects the "free variable" (shutter or aperture) to obtain the exposure that it metered.

So why are there two modes? You explained it yourself: So, for a given static scene, by me selecting any given aperture in Av, the CPU sets a corresponding shutter speed. And by me selecting any given shutter speed in Tv, the CPU sets a corresponding aperture.

There are two modes so that you can pick which variable you want to control. When you control the aperture, you are controlling the depth of field of the photograph. A large aperture, like f/1.4, will result in shallow depth-of-field—a sharp plane of focus, with things quickly becoming blurry outside that plane. A small aperture, like f/16, may result in almost everything appearing to be sharply focused.

If you shoot in shutter priority mode, you give up your depth of field control, but control the length of the exposure. By selecting a short exposure, you can guard against camera shake, or keep a moving subject sharp. By selecting a long exposure, you can deliberately blur the subject to show its motion.

So the point of having two exposure modes isn't that you get a different exposure in each of them, but that you exercise creative control over either the aperture or the shutter speed, whichever is more important to your photographic goal.